(5x+13)(x+23)=180

Solution for (5x+13)(x+23)=180 equation:

(5x+13)(x+23)=180

We move all terms to the left:

(5x+13)(x+23)-(180)=0

We multiply parentheses ..

(+5x^2+115x+13x+299)-180=0

We get rid of parentheses

5x^2+115x+13x+299-180=0

We add all the numbers together, and all the variables

5x^2+128x+119=0

a = 5; b = 128; c = +119;
Δ = b2-4ac
Δ = 1282-4·5·119
Δ = 14004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14004}=\sqrt{36*389}=\sqrt{36}*\sqrt{389}=6\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-6\sqrt{389}}{2*5}=\frac{-128-6\sqrt{389}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+6\sqrt{389}}{2*5}=\frac{-128+6\sqrt{389}}{10}
$